Mesoscopic superconducting systems have received attention as systems exhibiting complex physical phenomena for many years. Recently, these phenomena have been understood to have practical application in the field of quantum computing. See, e.g., A. Assime, G. Johansson, G. Wendin, R. Schoelkopf, and P. Delsing, “Radio-Frequency Single-Electron Transistor as Readout Device for Qubits: Charge Sensitivity and Backaction”, Phys. Rev. Lett. 86, p. 3376 (April 2001), and the references cited therein, and Alexandre Zagoskin, U.S. patent application Ser. No. 09/452,749, entitled “Permanent Readout Superconducting Qubit”, filed Dec. 1, 1999, which are herein incorporated by reference in their entirety.
Quantum computing generally involves initializing the states of N qubits (quantum bits), creating controlled entanglements among them, allowing these states to evolve, and reading out the states of the qubits after the evolution. A qubit is a quantum bit, the counterpart in quantum computing to the binary digit or bit of classical computing. Just as a bit is the basic unit of information in a classical computer, a qubit is the basic unit of information in a quantum computer. A qubit is conventionally a system having two degenerate (e.g., of equal energy) quantum states, wherein the quantum state of the qubit can be in a superposition of the two degenerate states. The two degenerate states are also referred to as basis states. Further, the two degenerate or basis states are denoted |0> and |1>. The qubit can be in any superposition of these two degenerate states, making it fundamentally different from a bit in an ordinary digital computer. If certain conditions are satisfied, N qubits can define an initial state that is a combination of 2N classical states. This initial state undergoes an evolution, governed by the interactions that the qubits have among themselves and with external influences, providing quantum mechanical operations that have no analogy with classical computing. The evolution of the states of N qubits defines a calculation or, in effect, 2N simultaneous classical calculations (e.g. conventional calculations as in those performed using a conventional computer). Reading out the states of the qubits after evolution completely determines the results of the calculations.
To appreciate the conditions necessary for N qubits to represent a combination of 2N classical states, the principles of superposition and entanglement must be introduced. Superposition may be described by considering a qubit as a particle in a magnetic field. The particle's spin may be either in alignment with the field, which is known as a spin-up state, or opposite to the field, which is known as a spin-down state. Changing the particle's spin from one state to another is achieved by using a pulse of energy, such as from a laser. If it takes one arbitrary unit of laser energy to change the particle's spin from one state to another, the question arises as to what happens if only a half a unit of laser energy is used and the particle is completely isolated from all external influences. According to quantum mechanical principles, the particle then enters a superposition of states, in which it behaves as if it were in both states simultaneously. Each qubit so utilized could take a superposition of both 0 and 1. Because of this property, the number of states that a quantum computer could undertake is 2n, where n is the number of qubits used to perform the computation. A quantum computer comprising 500 qubits would have a potential to do 2500 calculations in a single step. Conventional digital computers cannot perform calculations on a scale that even approaches 2500 calculations in any reasonable period of time. In order to achieve the enormous processing power exhibited by quantum computers, the qubits must interact each with each other in a manner that is known as quantum entanglement (entanglement).
Qubits that have interacted with each other at some point retain a type of connection and can be entangled with each other in pairs, in a process known as correlation. When a first qubit is entangled to a second qubit, the quantum states of the first and second qubits become correlated quantum mechanically. Entanglement is a quantum computing operation that has no analogue in classical computing. Once a pair of qubits has been entangled, information from only one of the qubits necessarily effects the state of the other qubit and vice versa. For example, once a pair of qubits are entangled, operations performed on one of the pair will simultaneously effect both qubits in the pair. Quantum entanglement allows qubits that are separated by larger distances to interact with each other instantaneously (not limited to the speed of light). No matter how great the distance between the correlated particles, they will remain entangled as long as they are isolated.
Taken together, quantum superposition and entanglement create an enormously enhanced computing power. Where a 2-bit register in an ordinary computer can store only one of four binary configurations (00, 01, 10, or 11) at any given time, a 2-qubit register in a quantum computer can store all four numbers simultaneously, because each qubit represents two values. If more qubits are entangled, the increased capacity is expanded exponentially.
Several physical systems have been proposed for the qubits in a quantum computer. One system uses molecules having degenerate nuclear-spin states. See N. Gershenfeld and I. Chuang, “Method and Apparatus for Quantum Information Processing,” U.S. Pat. No. 5,917,322, which is herein incorporated by reference in its entirety. Nuclear magnetic resonance (NMR) techniques can read the spin states. These systems have successfully implemented a search algorithm, see, e.g., M. Mosca, R. H. Hansen, and J. A. Jones, “Implementation of a quantum search algorithm on a quantum computer,” Nature 393, 344 (1998) and references therein, and a number-ordering algorithm, see, e.g., L. M. K. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, “Experimental realization of order-finding with a quantum computer,” preprint quant-ph/0007017, which is herein incorporated by reference in its entirety, and references therein. The number-ordering algorithm is related to the quantum Fourier transform, an essential element of both Shor's factoring algorithm (P. Shor, 1994, Proc. 35th Ann. Symp. On Found. Of Comp. Sci., pp. 124-134, IEEE Comp. Soc. Press, Los Alamitos, Calif.) and Grover's algorithm for searching unsorted databases (Grover, 1997, Phys. Rev. Lett. 78, p. 325, which is herein incorporated by reference in its entirety. However, expanding such systems to a commercially useful number of qubits is difficult. More generally, many of the current proposals will not scale up from a few qubits to the 102˜103 qubits needed for most practical calculations.
Unfortunately, current methods for entangling qubits are susceptible to loss of coherence. Loss of coherence is the loss of the phases of quantum superpositions in a qubit as a result of interactions with the environment. Thus, loss of coherence results in the loss of the superposition of states in a qubit. See, for example, Zurek, 1991, Phys. Today 44, p. 36; Leggett et al., 1987, Rev. Mod. Phys. 59, p. 1; Weiss, 1999, Quantitative Dissipative Systems, 2nd ed., World Scientific, Singapore; Hu et al; arXiv:cond-mat/0108339, which are herein incorporated by reference in their entirety, Entanglement of quantum states of qubits can be an important step in the application of quantum algorithms. See, for example, P. Shor, SIAM J. of Comput., 26:5, 1484-1509 (1997), which is herein incorporated by reference in its entirety. Current methods for entangling phase qubits require interaction of the flux in each of the qubits, see Yuriy Makhlin, Gerd Schon, Alexandre Shnirman, “Quantum state engineering with Josephson-junction devices,” LANL preprint, cond-mat/0011269 (November 2000), which is herein incorporated by reference in its entirety. This form of entanglement is sensitive to the qubit coupling with surrounding fields, which cause decoherence and loss of information.
As discussed above, currently proposed methods for read out, initialization, and entanglement of a qubit involve detection or manipulation of magnetic fields at the location of the qubit, which make these methods susceptible to decoherence and limits the overall scalability of the resulting quantum computing device. Thus, there is a need in the art for methods of entangling and otherwise controlling qubits. Such methods can be used to build efficient quantum registers where decoherence and other sources of noise are minimized but where scalability is improved.